Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.9 years, and standard deviation of 1.2 years. If 7 items are picked at random, 5% of the time their mean life will be less than how many years? Give your answer to one decimal place.

Answer #1

Solution :

Given that,

mean = = 3.9

standard deviation = = 1.2

Using standard normal table ,

n = 7

_{}
= 3.9

_{}
=
/
n = 1.2 /
7 = 0.4536

P(Z < z) = 5%

P(Z < -1.65) = 0.05

z = -1.65

= z *
_{}+
_{}
=-1.65 * 0.4536 + 3.9 = 3.2

The time their mean life will be less than **3.2
years**

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